Forma, Vol. 27 (No. 1), pp. 2536, 2012

Modelling Shape Languages with Type Constraint Systems

Dietrich Bollmann

Department of Architecture, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
E-mail address:

(Received August 9, 2011; Accepted November 14, 2011)

Abstract. Shape grammars are computational production systems used in various fields such as painting, sculpture and architecture for generating geometric shapes from a set of abstract rules. While similar to formal grammars as used in linguistics and computer science, they differ in using shapes instead of discrete symbols as representation. This makes them more intuitive and richer in possible interpretations than their symbolic counterparts but also more difficult to implement as computer programs. Using an example, this paper shows how a shape language can be modelled with a Type Constraint System (TCS), a formalism similar to the grammar formalism underlying the Head-Driven Phrase Structure Grammar (HPSG), widely used in computational linguistics for the modelling of natural languages. The result is a twolevel approach to the generation of shapes: an initial abstract symbolic representation is generated, from which the actual shapes are subsequently derived. While shape grammars and type constraint systems are not directly translatable into each other, the approach described in this paper can be implemented efficiently, making it easy to develop new shape languages and allowing for a wide range of interesting approaches to the generation of shapes.

Keywords: Generative Design, Formal Grammars, Shape Grammars, Type Constraint Systems

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